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In 2020, Olia et al. [Olia, Z. E. D. D., Gordji, M. E. and Bagha, D. E. (2020). Banach fixed point theorem on orthogonal cone metric spaces. FACTA Universitatis (NIS) Ser. Math. Inform, 35, 1239-1250] examined orthogonal cone metric spaces. They assumed that P is a normal cone with normal constant K and that self mapping T is orthogonal continuous on the orthogonal cone metric space X in their study. This study now presentes certain required definitions on orthogonal cone metric spaces that were not previously given in [9]. The examples that show the link between existing and new definitions have also been included. The results are also generalized by eliminating the normalcy condition and utilizing point orthogonal continuity instead of general orthogonal continuity in the major results of [9]. The fundamental finding of the study is then generalized by removing the requirement of orthogonal continuity and introducing normality. In addition, certain outcomes of stated theorems are proven, and some examples are provided to demonstrate these theorems. [ABSTRACT FROM AUTHOR]

In this paper, Caputo boundary value problems of order 3 < ζ ≤ 4 are investigated on the interval [0, 1]. By Guo-Krasnoselskii fixed point theorem, some criteria of existence and multiplicity of positive and decreasing solutions are established. The main novelty of the paper lies in its capability to achieve positive solutions while the corresponding Green’s function changes sign. Finally, two examples are provided to illustrate the application of these results. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the asymptotic stability of the trajectories governed by some delay differential inequalities on time scales. Based on time scale theory and the fixed-point theorem, some sufficient conditions are obtained for guaranteeing asymptotic stability. It is interesting that the inequalities studied in this paper include the generalized Halanay inequalities. Due to the fact that dynamic systems on a time scale unify discrete and continuous systems, the results of this paper have wider application value. Furthermore, some numerical examples verify the main results. [ABSTRACT FROM AUTHOR]

Abstract: An error is pointed out in the paper [J.R. Kang, Y.C. Kwun, J.Y. Park, Controllability of second order differential inclusion in Banach spaces, J. Math. Anal. Appl. 285 (2003) 537-550]. By an additional condition the considered system is controllable. [Copyright &y& Elsevier]

The work reported in this paper deals with the study of a coupled system for fractional terminal value problems involving ψ-Hilfer fractional derivative. The existence and uniqueness theorems to the problem at hand are investigated. Besides, the stability analysis in the Ulam–Hyers sense of a given system is studied. Our discussion is based upon known fixed point theorems of Banach and Krasnoselskii. Examples are also provided to demonstrate the applicability of our results. [ABSTRACT FROM AUTHOR]

This research paper presented a novel investigation into an implicit coupled system of fractional variable order, which has not been previously studied in the existing literature. The study focused on establishing and developing sufficient conditions for the existence and uniqueness of solutions, as well as the Ulam-Hyers stability, for the proposed coupled system without using semigroup property. By extending the existing conclusions examined for the Atangana-Baleanu-Caputo (ABC) operator, we contributed to advancing the understanding of variable-order fractional differential equations. The paper provided a solid theoretical foundation for further analysis, numerical simulations, and practical applications. The obtained results have implications for designing and controlling systems modeled using fractional variable order equations and serve as a basis for addressing a wide range of dynamical problems. The transformation techniques, qualitative analysis, and illustrative examples presented in this work highlight its unique contributions and potential to serve as a foundation for future research. [ABSTRACT FROM AUTHOR]

This paper aims to investigate the existence, uniqueness, and stability properties for a class of fractional weighted Cauchy-type problem in the variable exponent Lebesgue space Lp(.). The obtained results are set up by employing generalized intervals and piece-wise constant functions so that the Lp(.) is transformed into the classical Lebesgue spaces. Moreover, the usual Banach Contraction Principle is utilized, and the Ulam-Hyers (UH) stability is studied. At the final stage, we provide an example to support the accuracy of the obtained results. [ABSTRACT FROM AUTHOR]

This paper aims to investigate a class for nonlocal fractional boundary value problem on an infinite interval due to its importance in provide a powerful tool for mathematical modeling of complex phenomena in science. New existence results are acquired for the given problem by using the Krasnosel'skii's fixed point theorem. Moreover, sufficient conditions are obtained as well as a modified compactness criterion that guarantees the existence of at least one solution. In addition, an illustrative example is given in the final part of the paper. [ABSTRACT FROM AUTHOR]

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In this paper we prove the existence of solutions for fractional order functional and neutral functional differential equations with infinite delay principles combined with a technique based on vector-valued metrics and convergent to zero matrices. [ABSTRACT FROM AUTHOR]

In this paper, we present a result on the existence of asymptotically stable solutions of infinite systems (IS) of quadratic Hammerstein integral equations (IEs). Our study will be conducted in the Banach space of functions, which are continuous and bounded on the half-real axis with values in the classical Banach sequence space consisting of real bounded sequences. The main tool used in our investigations is the technique associated with the measures of noncompactness (MNCs) and a fixed point theorem of Darbo type. The applicability of our result is illustrated by a suitable example at the end of the paper. [ABSTRACT FROM AUTHOR]

In this paper, we study a quantum difference coupled impulsive system with respect to another function. Some quantum derivative and integral asymmetric graphs with respect to another function are shown to illustrate the behavior of parameters. Existence and uniqueness results are established via Banach contraction mapping principle and Leray–Schauder alternative. Examples illustrating the obtained results are also included. Our results are new and significantly contribute to the literature to this new subject on quantum calculus on finite intervals with respect to another function. [ABSTRACT FROM AUTHOR]

The paper investigated the exact controllability of delayed fractional evolution systems of order α ∈ (1, 2) in abstract spaces. At first, the exact controllability result is obtained when the nonlinear term f is locally Lipschitz continuous. Then, the certain compactness conditions and the measure of noncompactness conditions were applied to demonstrate the exact controllability of the concerned problem. The discussion was based on the fixed point theorems and the cosine family theory. [ABSTRACT FROM AUTHOR]

The primary focus of this paper is threefold: first, to investigate the existence of mild solutions; second, to analyze the topological and geometrical structure of the solution sets; and third, to determine the continuous dependence of the solution for second-order semilinear integro-differential inclusion. In this study, we employ Bohnenblust–Karlin’s fixed point theorem in conjunction with the theory of resolvent operators, as presented by Grimmer. An illustrative example is employed to showcase the achieved outcomes. [ABSTRACT FROM AUTHOR]

The main aim of this paper is to study the Cauchy problem for nonlinear differential equations of fractional order containing the weighted Riemann-Liouville fractional derivative of a function with respect to another function. The equivalence of this problem and a nonlinear Volterratype integral equation of the second kind have been presented. In addition, the existence and uniqueness of the solution to the considered Cauchy problem are proved using Banach's fixed point theorem and the method of successive approximations. Finally, we obtain a new estimate of the weighted Riemann-Liouville fractional derivative of a function with respect to functions at their extreme points. With the assistance of the estimate obtained, we develop the comparison theorems of fractional differential inequalities, strict as well as nonstrict, involving weighted Riemann-Liouville differential operators of a function with respect to functions of order d, 0 < d < 1. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the existence of positive periodic solutions of a third-order nonlinear integrodifferential equation with distributed delays, by using the Green function and the Krasnosel'skii fixed point theorem in cones of Banach spaces, providing new results on this field. Three examples are analyzed to illustrate the effectiveness of the abstract results. [ABSTRACT FROM AUTHOR]

This research paper study the existence, uniqueness and Ulam–Hyers stability of the solutions of a certain system of thegeneralized Caputo fractional differential equations in the context of the generalized metric spaces. The existence and uniqueness theorems are proved by using the Krasnoselskii’s and Perov’s fixed point theorems under the Bielecki norm with a Lipschitzian matrix in the generalized metric spaces. Moreover, the Ulam–Hyers stability analysis is conducted based on the Urs’s criterion. An example, lastly, is proposed to check the efficiency of the above-mentioned theorems. The results are novel and provide extensions to some of the findings known in the literature. [ABSTRACT FROM AUTHOR]

Circular network structure is widely used in neural network, image processing, computer vision and bioinformatics. For example, recurrent neural network is a kind of neural network with a circular structure that can be used to process temporal data. It has a wide range of applications in natural language processing, speech recognition, music generation, etc. In this paper, in order to reduce the complexity of the presentation, we study a class of Hilfer-type fractional differential system and differential inclusion with coupled integral boundary value conditions on the simplest circular graph. First, two existence results of Hilfer-type fractional differential system are proved by some known fixed point theorems. Further, the existence results of convex and non-convex multivalued mappings are obtained by using Leray–Schauder nonlinear alternative and Covitz–Nadler fixed point theorem, respectively. At last, two examples are given to verify our theoretical results. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to analyze the solvability of a class of stochastic functional integral equations by utilizing the measure of non-compactness with Petryshyn’s fixed point theorem in a Banach space. The results obtained in this paper cover numerous existing results concluded under some weaker conditions by many authors. An example is given to support our main theorem. [ABSTRACT FROM AUTHOR]

This paper investigates the existence and uniqueness of solutions for a system of Hilfer-Hadamard sequential fractional differential equations using standard fixed-point theorems. We apply the Leray-Schauder alternative and Banach's contraction mapping principle to obtain the existence and uniqueness results for the given problem. Additionally, we discuss illustrative examples. [ABSTRACT FROM AUTHOR]

In this paper, we use a novel approach to study the existence, uniqueness, and stability of solutions (EUSS) to a Cauchy-type problem of nonlinear fractional differential equations (FrDiEq) of variable order with infinite delay (CPNFDEVOID). Contrary to the techniques taken in the literature, which were centered on the usage of the concept of generalized intervals and the idea of piecewise constant functions, our approach is straightforward and based on a novel fractional operator that is more appropriate and demonstrates the solvability and stability of the main problem under less restrictive presumptions. The results are achieved in this paper by using Fixed Point Theory (FPT). The application, which includes an example and supporting images, concludes the paper. [ABSTRACT FROM AUTHOR]

In this paper, we studied the generalizations of quantum calculus on finite intervals. We presented the new definitions of the quantum derivative and quantum integral of a function with respect to another function and studied their basic properties. We gave an application of these newly defined quantum calculi by obtaining a new Hermite-Hadamard inequality for a convex function. Moreover, an impulsive boundary value problem involving quantum derivative, with respect to another function, was studied via the Banach contraction mapping principle. [ABSTRACT FROM AUTHOR]

In this paper, we explore the stability of a new class of Caputo-type fractional stochastic delay differential systems with Poisson jumps. We prove the Hyers–Ulam stability of the solution by utilizing a version of fixed point theorem, fractional calculus, Cauchy–Schwartz inequality, Jensen inequality, and some stochastic analysis techniques. Finally, an example is provided to illustrate the effectiveness of the results. [ABSTRACT FROM AUTHOR]

Monge–Ampère equations have important research significance in many fields such as geometry, convex geometry and mathematical physics. In this paper, under some superlinear and sublinear conditions, the existence of nontrivial solutions for a system arising from Monge–Ampère equations with two parameters is investigated based on the Guo–Krasnosel'skii fixed point theorem. In the end, two examples are given to illustrate our theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, we consider the existence of positive solutions for a system of fractional q -difference equations with generalized p -Laplacian operators. By using Guo-Krasnosel'skii fixed point theorem, we obtain some existence results of positive solutions for this system with two parameters under some different combinations of superlinearity and sublinearity of the nonlinear terms. In the end, we give two examples to illustrate our main results. [ABSTRACT FROM AUTHOR]

In this paper, we study the existence and uniqueness of a positive solution for a boundary value problem of nonlinear fractional integro-differential equations involving a generalized version of the Riemann–Liouville fractional derivative with respect to another function ψ and integral boundary conditions. Using the Banach's contraction principle and Schaefer's fixed point theorem together with the upper and lower solution method we prove our main results. Finally, an example is presented to illuminate our theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, the existence of the solutions of a class of weakly singular integral equations in Banach algebra is investigated. The basic tool used in investigations is the technique of the measure of non-compactness and Petryshyn's fixed point theorem. Also, for the applicability of the obtained results, some examples are given. [ABSTRACT FROM AUTHOR]

In this paper, we study a matrix equation involving the matrix geometric mean . We study several properties and inequalities for the unique solution of such an equation. We also use the weighted geometric mean to define a new quantum Hellinger divergence and show that the new quantum divergence satisfies the Data Processing Inequality. [ABSTRACT FROM AUTHOR]

In this paper, we present a new fixed-point result to draw conclusions about the existence and uniqueness of the solution for a nonlinear Fredholm integral equation of the second kind with non-differentiable Nemytskii operator. To do this, we will transform the problem of locating a fixed point for an integral operator into the problem of locating a solution of an integral equation. Thus, assuming conditions on the Nemytskii operator, we will obtain a global convergence domain for the solution of the considered integral equation, taking for this a uniparametric family of derivativefree iterative processes with quadratic convergence. This result provides us a new fixed-point result for the integral operator considered. [ABSTRACT FROM AUTHOR]

In the present paper, we mainly focus on an iterative erythropoiesis model with a nonlinear harvesting term involving a time-varying delay. Under certain conditions and by the Schauder fixed point theorem, we show that the existence of positive periodic solutions can be guaranteed and based on the Banach fixed point theorem, we establish the existence as well as the continuous dependence on parameters theorems of the unique solution. Moreover, two examples are provided to validate the correctness of our outcomes. Our theoretical findings extend and improve several related ones in the existing literature. [ABSTRACT FROM AUTHOR]

In this paper, we study the main results of existence and uniqueness of mild solutions of fractional Volterra integrodifferential equation involving Caputo fractional derivative of special class n - 1 < α ≤ n, n > 1. Furthermore, the various type of dependency of mild solutions of the proposed problem have been studied such as dependence on given initial data, continuously depends on the functions involved in the right side of the problem and on real parameters. The result of existence and uniqueness is obtained with help of well known Banach contraction principle and the integral inequality established by B. G. Pachpatte which provides explicit bound on the unknown function. A suitable example is given to demonstrate the obtained results. [ABSTRACT FROM AUTHOR]

Recently, fractional q-difference equations on infinite intervals have attracted much attention due to their potential applications in many fields. In this paper, we investigate a class of nonlinear high-order fractional q-difference equations with integral boundary conditions on infinite intervals, where the nonlinearity contains Riemann–Liouville fractional q-derivatives of different orders of unknown function. By means of Schaefer fixed point theorem, Leray–Schauder nonlinear alternative and Banach contraction mapping principle, we acquire the existence and uniqueness results of solutions. Furthermore, we establish the Hyers–Ulam stability for the proposed problem. In the end, several concrete examples are utilized to demonstrate the validity of main results. [ABSTRACT FROM AUTHOR]

In this paper, we aim to prove the existence and uniqueness of the mean square solution to the Caputo fractional random boundary value problem by using the fixed point theorems. Moreover, we introduce the Ulam–Hyers stability and generalized Ulam–Hyers stability for this problem. Finally, we give an example to illustrate our results. [ABSTRACT FROM AUTHOR]

In this paper, we are interested in the study of the existence and uniqueness of positive solutions to the nonlinear singular fractional differential equation D 0 + α u (t) + f (t , u (t) , (H u) (t)) = 0 with 0 < t < 1 , where D 0 + α denotes the classical Riemmann Liouville derivative, under the integral boundary conditions u (0) = u ′ (0) = ⋯ = u (n - 2) (0) = 0 and u (1) = λ ∫ 0 1 u (s) d s , where λ ∈ (0 , α) , H is an operator defined on C [ 0 , 1 ] into itself and f : (0 , 1 ] × [ 0 , ∞) × [ 0 , ∞) → [ 0 , ∞) is a continuous function which can have a singularity at (0, x, y). To state our results, we use a fixed point theorem recently proved. Finally, we present some examples illustrating the results obtained. [ABSTRACT FROM AUTHOR]

In this paper, we discuss the existence and uniqueness of solution of the singular quadratic integral equation (SQIE). The Fredholm integral term is assumed in position with singular kernel. Under certain conditions and new discussions, the singular kernel will tend to a logarithmic kernel. Then, using Chebyshev polynomial, a main of spectral relationships are stated and used to obtain the solution of the singular quadratic integral equation with the logarithmic kernel and a smooth kernel. Finally, the Fredholm integral equation of the second kind is established and its solution is discussed, also numerical results are obtained and the error, in each case, is computed. [ABSTRACT FROM AUTHOR]

In this paper, we consider the initial and boundary value problem for the beam equation with the viscosity term and the compressible stress function for the nonlinear strain. We have already proved existence and uniqueness of weak solutions to the problem without the viscosity term and having a Lipschitz continuous stress function. Our aims of the present paper are to prove existence for strong and weak solutions by applying the fixed point theory and the approximation method, and to establish uniqueness by the standard Gronwall argument. [ABSTRACT FROM AUTHOR]

In this paper, optimal control problems for a class of stochastic functional integral-differential equations in Hilbert spaces are investigated. First, the existence of mild solutions is investigated using stochastic analysis theory, fixed point theorems, and Grimmer's resolvent operator theory. Following that, the existence requirements of optimal pairs of systems governed by stochastic partial integro-differential equations with infinite delay are discussed. The results are achieved by the use of a combination of Lipschitz and Carathéodory conditions. At the end of the paper, an illustration is supplied to help highlight the key findings. [ABSTRACT FROM AUTHOR]